Only odd anglers read The Times (4)
I believe the answer is:
ages
'the times' is the definition.
(age is a kind of time)
'only odd anglers' is the wordplay.
'only odd' indicates alternate letters.
The alternating letters of 'anglers' are 'AGES'.
'read' is the link.
(Other definitions for ages that I've seen before include "(What seems) a very long time" , "Historic periods or prolonged time" , "Matures" , "Grows old like sage" , "Indefinitely long time" .)